Nicholas Williams

Look, I have been to Oberwolfach in the snow my email address
Since the beginning of September 2022, I have been a Postdoctoral Research Associate at Lancaster University working with David Pauksztello. During August and September 2023, I was also a visiting researcher at the Okinawa Institute of Science and Technology — in fact, the first ever visitor on a TSVP thematic program at OIST, thanks to a typhoon.

I received my doctorate from the University of Cologne in 2022 under the supervision of Sibylle Schroll. Following that, I was a JSPS short-term postdoctoral research fellow at the University of Tokyo working with Osamu Iyama from late May to late August 2022.

My research focuses on the representation theory of finite-dimensional algebras and combinatorics. In the representation theory of finite-dimensional algebras I am particularly interested in In combinatorics, I am particularly interested in I am naturally interested in the interplay between these two areas too.

I am organising this conference on simple-mindedness, silting, and stability from 8th-12th July 2024 in Ambleside in the North of England with David Pauksztello and Raquel Coelho Simões.

You can find a copy of my CV here (updated 6/6/24).

GitHub, Google Scholar, Math Genealogy, ORCID, ResearchGate, Scopus.

In my spare time, I like singing karaoke.

Pronouns: he/him/his.

Preprints

1/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence, (with Omar Kidwai) arXiv.
9/2023 Steenrod operations via higher Bruhat orders, (with Guillaume Laplante-Anfossi) arXiv.
2/2023 A geometric perspective on the τ-cluster morphism category, (with Sibylle Schroll, Aran Tattar, and Hipolito Treffinger) arXiv.
1/2023 A structural view of maximal green sequences, (with Mikhail Gorsky) arXiv.

Journal publications

To appear The two higher Stasheff–Tamari orders are equal
Journal of the European Mathematical Society. arXiv.
5/2024 A survey of congruences and quotients of partially ordered sets
EMS Surveys in Mathematical Sciences. DOI, arXiv.
4/2024 Triangulations of prisms and preprojective algebras of type A, (with Osamu Iyama)
International Mathematics Research Notices. DOI, arXiv.
4/2024 Stability spaces of string and band modules, (with Sibylle Schroll, Aran Tattar, Hipolito Treffinger, and Yadira Valdivieso)
Journal of Pure and Applied Algebra. DOI, arXiv.
6/2023 Quiver combinatorics and triangulations of cyclic polytopes
Algebraic Combinatorics. DOI, arXiv.
2/2023 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Electronic Journal of Combinatorics. DOI, arXiv.
10/2022 New interpretations of the higher Stasheff–Tamari orders
Advances in Mathematics. DOI, arXiv.
9/2021 The combinatorics of tensor products of higher Auslander algebras of type A, (with Jordan McMahon)
Glasgow Mathematical Journal. DOI, arXiv.

Conference proceedings

2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Cluster Algebras and Its Applications, Oberwolfach Reports. Link.
2023 The higher Stasheff–Tamari orders in representation theory
Representations of Algebras and Related Structures. DOI, arXiv.
2023 Studying Triangulations of Even-Dimensional Cyclic Polytopes via Directed Graphs
Proceedings of the 34th International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire 89B (2023), Art. 4. Link.
2022 Triangulations of cyclic polytopes and the higher Auslander algebras of type A
Various issues on representation theory and related topics, RIMS Kōkyūroku No. 2234. Link.
2021 The first higher Stasheff–Tamari orders are quotients of the higher Bruhat orders
Proceedings of the 33rd International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire 85B (2021), Art. 6. Link.

Other publications

7/2022 Microthesis: Triangulations of cyclic polytopes in representation theory
London Mathematical Society Newsletter, No. 501, 33-34. Link.
4/2022 Higher-dimensional combinatorics in representation theory
Doctoral thesis, University of Cologne. Link.

Recent talks

5/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Algebraic Geometry Days in Glasgow, University of Glasgow
4/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Leeds Algebra Seminar, University of Leeds
4/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Algebra and Number Theory Seminar, University of Vienna
3/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Paris Algebra Seminar, Institut de Mathématiques de Jussieu-Paris Rive Gauche
1/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Clusters and their Applications in the North, University of Glasgow
1/2024 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Cluster Algebras and Its Applications, Mathematisches Forschungsinstitut Oberwolfach
10/2023 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
Sheffield Geometry and Physics Seminar, University of Sheffield
10/2023 Donaldson–Thomas invariants for the Bridgeland–Smith correspondence
EGRET seminar, University of Edinburgh
9/2023 Donaldson–Thomas theory of quivers with potential
Exact Asymptotics Theoretical Sciences Visiting Program, Okinawa Institute of Science and Technology
8/2023 Higher-dimensional cluster combinatorics and representation theory
OIST Representation Theory Seminar, Okinawa Institute of Science and Technology
8/2023 Triangulations of cyclic polytopes through the lens of reconfiguration
Minisymposium on Combinatorial Reconfiguration, International Congress on Industrial and Applied Mathematics, Waseda University, Tokyo
8/2023 Combinatorics of KP solitons
Exact Asymptotics Theoretical Sciences Visiting Program, Okinawa Institute of Science and Technology
7/2023 Triangulations of prisms and preprojective algebras of type A
Combinatorial Representation Theory in Leeds, University of Leeds
6/2023 A structural view of maximal green sequences
Cluster Structures in the North, University of Central Lancashire
4/2023 A structural view of maximal green sequences
Maurice Auslander Distinguished Lectures and International Conference
2/2023 A structural view of maximal green sequences
Algebra Group Seminar, University of Cologne
12/2022 Cyclic polytopes and representation theory
Representation Theory of Algebras session, Canadian Mathematical Society Winter Meeting, Toronto
11/2022 The higher Stasheff–Tamari orders on triangulations of cyclic polytopes
Séminaire du LaCIM, Université du Québec à Montréal
11/2022 Cyclic polytopes and representation theory
Geometry and Mathematical Physics Seminar, University of Birmingham
11/2022 Cyclic polytopes and representation theory
Pure Mathematics Seminar, Lancaster University
10/2022 Mutation in higher cluster categories
Seminar@Aarhus, Aarhus University
9/2022 A structural approach to maximal green sequences
Silting theory, Algebras and Representations, Charles University, Prague

Translations

I have translated a couple of papers of Carathéodory from German into English. I make no claim to any of the mathematics in these papers. It is also not impossible that I have introduced errors in the process of translation.

Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen
Constantin Carathéodory
Mathematische Annalen (1907), Volume: 64, pp. 95–115.
Original, Translation
Über den Variabilitätsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen
Constantin Carathéodory
Rendiconti del Circolo Matematico di Palermo (1911), Volume: 32, pp. 193–217.
Original, Translation

Conference organisation

I organised this conference with Aran Tattar.
Conference poster